How to simplify rational expressions

(a - 1)/(3a - 2)

Step-by-step explanation:

First lets find a common factor in all of those numbers. We can factor out 'a'!

We're then left with (2a^2 + a - 3)/(6a^2 + 5a - 6)

Now we need to find some more factors.

Lets start at the top.

Factors of -3 are -1, 3, -3, 1

We can therefore factorize the top line to be:

(2a + 3)(a - 1)/(6a^2 + 5a -6)

Sweet! Now lets see if one of those two factors is a factor of the bottom line.

Factors of -6 are -1, 6, 2, -3, -2, 3, -6, 1

We can factorize the bottom line!

(2a + 3)(a - 1)/(3a - 2)(2a + 3)

Now to simplify

= (a - 1)/(3a - 2)

annnd we are done.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west